Elastic actuator for precise force control

ABSTRACT

The invention provides an elastic actuator consisting of a motor and a motor drive transmission connected at an output of the motor. An elastic element is connected in series with the motor drive transmission, and this elastic element is positioned to alone support the full weight of any load connected at an output of the actuator. A single force transducer is positioned at a point between a mount for the motor and an output of the actuator. This force transducer generates a force signal, based on deflection of the elastic element, that indicates force applied by the elastic element to an output of the actuator. An active feedback force control loop is connected between the force transducer and the motor for controlling the motor. This motor control is based on the force signal to deflect the elastic element an amount that produces a desired actuator output force. The produced output force is substantially independent of load motion. The invention also provides a torsional spring consisting of a flexible structure having at least three flat sections each connected integrally with and extending radially from a central section. Each flat section extends axially along the central section from a distal end of the central section to a proximal end of the central section.

GOVERNMENT RIGHTS IN THE INVENTION

This invention was made with U.S. government support under contract No.959333, awarded by the Jet Propulsion Laboratory of the U.S. Departmentof Energy. The U.S. Government has certain rights in this invention.

FIELD OF THE INVENTION

This invention relates to actuators for use in, for example, roboticapplications, and more particularly relates to force generation andcontrol in robotic actuators.

BACKGROUND OF THE INVENTION

Actuation of a robotic element is optimally provided by an actuator thatis light weight and low cost and that exhibits capabilities of highpower and force or torque generation, shock tolerance, and above all,precise force control and force control stability. Actuators that areoverly bulky or heavy put a strain on the other elements of the systemwithin which they reside; the remaining actuators in the system mustaccommodate the weight with additional power. As robotic and automatedsystems continue to increase in size, complexity and functionality, thenumber of system components so too increases, resulting in the need foreconomically-priced system parts.

In addition, as the modes of interaction between robotic systems andtheir environments increase in freedom and complexity, high power, highforce or torque generation is required to provide capabilities in a widerange of robotic load manipulation tasks. But at the same time, however,the force or torque generation must be precisely controlled to enableinteraction with the robot's environment without causing damage toeither the environment or the robot. Indeed, shock tolerance is requiredof robotic actuator systems because the chance of unexpected orunpredictable high-force interactions with task and load manipulationenvironments is greatly increased in such complex applications.

Heretofore these actuator attributes have been in contradiction. Forexample, to achieve a decrease in actuator weight, gears areconventionally introduced in an actuator employing a motor. Although agear train does lighten the system by allowing for use of a smallermotor operating at higher speeds, it also sensitizes the system to shockloads; shock-induced damage of gear trains is known to be one of themost common modes of actuator failure. In an effort to enhance geartrain strength to reduce gear damage, precise materials and designs areoften employed for gear systems. Typically such systems areprohibitively expensive and therefore are not acceptable for commonrobotic actuation applications. As a result, design efforts toward astrong, inexpensive, light weight, shock resistant actuator thatprovides precise force control have been suboptimal.

SUMMARY OF THE INVENTION

The invention provides an actuator that overcomes limitations ofconventional actuators to achieve precise force control with a strong,inexpensive, light weight and shock resistant actuator design.

In accordance with the invention, in one aspect, there is provided anelastic actuator consisting of a motor and a motor drive transmissionconnected at an output of the motor. An elastic element is connected inseries with the motor drive transmission, and this elastic element ispositioned to alone support full weight of any load connected at anoutput of the actuator. A single force transducer is positioned at apoint between a mount for the motor and an output of the actuator. Thisforce transducer generates a force signal, based on deflection of theelastic element, that indicates force applied by the elastic element toan output of the actuator. An active feedback force control loop isconnected between the force transducer and the motor for controlling themotor. This motor control is based on the force signal to deflect theelastic element an amount that produces a desired actuator output force.The produced output force is substantially independent of load motion.

Unlike conventional actuators, the elastic actuator of the inventionprovides force generation and control directly through a series elasticelement that itself supports the load of the actuator. This arrangementsubstantially shields the actuator motor and transmission from shockloads, while at the same time provides the ability to very preciselycontrol force produced by the actuator; indeed, the produced force issubstantially independent of any motion of the load. The series elasticelement enables an actuator geometry that is elegantly simple, resultingin an actuator system that is light weight, easy to manufacture, andinexpensive. The series elastic element also enables an actuatorgeometry that is quite strong.

In preferred embodiments, the force transducer consists of a straingauge, preferably positioned on the elastic element, or a potentiometer.Preferably, the elastic element consists a linear spring or a torsionalspring.

In other aspects, the invention provides a torsional spring consistingof a flexible structure having at least three flat sections eachconnected integrally with and extending radially from a central section.Each flat section extends axially along the central section from adistal end of the central section to a proximal end of the centralsection.

In preferred embodiments, the torsional spring flexible structure has atleast three flat sections each connected integrally with and extendingradially from the central section. Preferably, the flexible structurecomprises steel and has four flat sections each connected integrallywith the central section at a right angle with respect to adjacent flatsections. In other preferred embodiments, the torsional spring includesa first mounting block integrally connected with the distal end of thecentral section and a second mounting block integrally connected withthe proximal end of the central section. Preferably, the first andsecond mounting blocks each include a central annulus. In otherpreferred embodiments, the torsional spring consists of a cylindricalsection extending from the central section proximal end to the centralsection distal end. The cylindrical section is integrally connected witha radial edge of each flat section.

The elastic actuator and spring provided by the invention are applicableto a wide range of robotics, automation, and actuation applicationswhere, e.g., a robotically actuated arm, hand, leg, or foot interactswith an unstructured and/or unpredictable environment.

Other features and advantages of the invention will be apparent from adescription of a preferred embodiment, and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically illustrates the components of an example elasticactuator in accordance with the invention;

FIG. 2 schematically illustrates the actuator of FIG. 1 in more detail;

FIGS. 3A-3F schematically illustrate examples of torsion springsprovided by the invention;

FIG. 4 schematically illustrates the actuator of FIG. 2 including aforce sensing mechanism in accordance with the invention;

FIGS. 5A and 5B schematically illustrate positioning of strain gauges ona torsion spring in accordance with the invention;

FIG. 6 is a block diagram of the components in the force control systemprovided by the invention;

FIG. 7 is a block diagram of the control function components in thesystem of FIG. 6,;

FIG. 8 schematically illustrates a force model for an elastic actuatorin accordance with the invention;

FIG. 9 is a block diagram of the control function components and outputparameters of the force control system provided by the invention;

FIGS. 10A-10E are plots of force generated by an elastic actuator inaccordance with the invention in response to a force command, as afunction of time;

FIGS. 11 and 12A-12B schematically illustrate three alternative elasticactuator configurations in accordance with the invention;

FIG. 13 schematically illustrates a pulley-based elastic actuator inaccordance with the invention; and

FIGS. 14A-14F schematically illustrate examples of force sensingconfigurations for an elastic tendon actuator in accordance with theinvention.

DESCRIPTION OF A PREFERRED EMBODIMENT

FIG. 1 illustrates the fundamental components of an elastic,force-controlled actuator 10 in accordance with the invention. Theactuator 10 includes a driving source for force generation, e.g., amotor 12, which may be geared with a geartrain, or gearbox 14. As willbe understood by those in the field of actuator design, such a geartrain may be integral to the motor source and in any case is notrequired for all applications. An elastic spring element 16 is linked inseries with the output of the gearbox 14, or if no gearbox is employed,is linked in series directly with the motor 12. The load 18 to bemanipulated by the actuator 10 is then itself linked in series with theelastic element 16. This elastic spring element introduces at theinterface between the actuator 10 and the load 18 a series elasticitythat provides the ability to achieve precise control of the forceapplied to the load, as explained below. The series elastic element maybe linked to the load through a transmission element (not shown); such atransmission element must, however, be characterized as aback-driveable, low friction, low backlash transmission.

In general, precise force control is accomplished in the actuator by wayof controlling the series elastic element such that a desired forceoutput of the actuator is developed by the spring. As will be shown,this control scheme provides for more accurate, more stable, and lessnoisy force control than is achieved by conventional, stiff actuators.In addition, the series elastic element acts as a low pass filter toshock loads, thereby protecting the gearbox and motor from damage. Thestrength of gear teeth is quite often the factor limiting the strengthof conventional actuators. This limitation is inherently compounded bythe reducing action of the gearbox; the gear reduction increases theeffective inertia of the motor, whereby large forces can result fromshock loads. Indeed, gearbox failures due to this effect are common forconventional actuators. The series elastic element low-pass filters suchshock loads before they reach the gearbox, whereby the motor and thegearbox are largely isolated from shock.

A first embodiment of the elastic actuator is shown in FIG. 2. Itconsists of a motor and gearbox 12, 14, having an output shaft 20connected directly to a torsion spring 16. The motor may be outfittedwith an encoder (not shown) if desired for a specific application; suchan encode is not, however, required for the actuator control system ofthe invention. One suitable motor and gearbox is the MicroMo 3557K motorand MicroMo 30/1 gearbox, which may both be obtained from MicroMo, Inc.Preferably, the motor exhibits a high torque-to-current ratio, a highmaximum current and stall torque, good heat dissipation, low mass, andlow friction from brushes, etc. However, for any motor employed, theperformance of the elastic actuator always exceeds the performance ofthe motor system; a motor system of any quality is thus accommodated bythe actuator. The transmission, e.g., the motor gearbox, is preferablycompact, and preferably exhibits low backlash. The gearbox output ispreferably of a high torque rating. While as explained above the springacts to insulate the gearbox and motor from shock loads, therebyaccommodating a gearbox transmission of poor quality, a high qualitytransmission is nevertheless preferred.

The torsion spring is mounted between bearings (not shown) on the motorgearbox and shaft and the actuator output element 18. This outputelement is supported in a bearing 24, the spring passing through thecenter of the bearing axle 26 to conserve space requirements for theactuator system.

Considering the particular geometry and properties of the torsionalspring element, such a spring may be constructed of, e.g., steel,aluminum, delrin, or nylon 66, or other suitable material. Preferably,the spring is an integral structure that is light-weight and compact,and exhibits a desired stiffness for a given application. Note that thespring actually carries the actuator load; as a result, the springoptimally is of a high load carrying capacity, or at least a carryingcapacity suitable for a given load application. In addition, it ispreferable that the spring exhibit no hysterisis, i.e., no energy lossper compression cycle, and that the spring be of a geometry that is easyto attach between the actuator driving mechanism and the actuator loadelement.

While the torsion spring element may embody any convenient geometry, itis preferable that the spring embody a cross shape, flat plate shape, orcomposite plate shape. It is found that for torsion, cylindrical springsare too efficient, i.e., a given cylindrical spring design that attainsa desired strength is too stiff. FIG. 3 illustrates various preferablyspring designs. In a first composite plate spring 30, shown in FIG. 3A,strips of shim steel 32, i.e., hardened steel strips, are fastened byway of clamps (not shown) to form an interconnected stack of plates.Each plate 32 is of a thickness t, a width b, and a length 1. The yieldangle of the composite spring overall is a function of t and l; thus,the spring stiffness is altered by adjusting the width of the strips andthe number of strips used.

One example composite plate spring consists of 6 strips having a widthof 0.55", a length of 1.9", and a thickness of 0.032". Spacers eachhaving a thickness of 0.01 " are placed between the strips to preventthem from rubbing against each other. The force produced by such aspring is roughly a linear function of the twist angle of the stack, andmay exhibit a small degree of hysteresis. Because the outermost springstrips are in a combination of tension and torsion, rather than puretorsion, the composite stack spring is found to exhibit a higher degreeof stiffness than theoretically predicted.

An integral spring structure in accordance with the invention that forsome applications may be preferable to this composite spring stack isshown in FIGS. 3B-3D. This integral spring design consists of anintegral cross spring 36, made up of a vertical sheet 38, of thickness tand height h, which intersects a horizontal sheet 40, of width b andthickness t, at its center. The vertical and horizontal sheets are bothof a length l. This integral cross-shaped spring is easy to manufactureand requires no assembly of composite sub-pieces. This providesimportant advantages because bearings, spacers, or other links needed tohold the pieces of a composite spring structure together absorb energy;the integral spring, in contrast, requires no such links.

The integral cross spring 36 provided by the invention is torsionallyflexible but flexurally rigid, meaning that the spring can support abending load. The spring is also strong, in that it is of a lowstiffness but can carry a large load before yielding. The spring ispreferably formed of steel, e.g., AISI/SAE 4142, because steel has adefinite, predictable yield point, and because steel can beheat-treated, if desired, to produce a specifically desired elasticcharacteristic for a given application.

The yield angle, maximum torque, and stiffness of the cross spring maybe modeled by approximating the cross spring as an equivalent flat plateof width (b+h), length l, and thickness t. The yield angle, θ_(max),spring stiffness, k_(spring), and maximum torque, T_(max), are thengiven, respectively, as: ##EQU1## where τ_(max) is the maximum shearstress accommodated by the spring and G is the shear modulus of thespring material.

While it is found that the integral cross spring does indeed obey thesegeneral relationships, the cross spring exhibits a slightly lowerstiffness than is predicted. This is due to the fact that in the crossspring an appreciable amount of the spring material is located near tothe spring's twist axis, which inherently results in reduction ofstiffness. The cross spring is similarly found to withstand a largermaximum angle of twist than is predicted. The stiffness and maximumallowable twist angle determine the maximum torque that can be carriedby the spring. Although the stiffness is found to be less thanpredicted, the increased maximum twist angle results in a maximum torquecapability that is greater than that of a flat plate by a factor ofabout 1.6. This increased torque capability, together with its compactdesign, makes the integral cross spring uniquely well-suited for use inan elastic actuator system.

Preferably, the corners of the cross shape of the spring are machined tobe sharp. This consideration is required because a section of the springwill yield more easily if there is too large a radius at the center. Inaddition, the sharp corners act to limit the mass in the center of thespring. If the amount of mass in the center of the cross is larger thana critical mass, the cross spring behaves like a rod, whereby thedisadvantages associated with a conventional cylindrical spring, e.g.,high stiffness and low yield, are produced.

Referring to FIGS. 3C and 3D, the integral cross spring of the inventionmay be machined to provide flat end pieces with holes or other geometryfor fastening the spring to, e.g., the motor and the load in an actuatorsystem. In one such geometry, the cross spring 36 includes rectangularend portions 42. As shown in FIG. 3D, the cross-shaped section may betapered at sloping corners 46 to define end portions 42 that are morenarrow than the spring center section. A central hole 44 may be formedin either or both of the rectangular ends for providing a graspingmechanism.

The end portions 42 of the integral cross spring 36 both support theends of the cross shape and transfer the load to the spring; they alsoprovide a very convenient means for grasping and fastening the spring toa load member. As a practical matter, the end portions also provide ananchor means for holding on to as the central cross geometry of thespring is machined during manufacture.

In variations of the integral cross spring of the invention, thecross-shaped section may be machined out of a circular section or othergeometric shape. For example, as shown in FIG. 3E, the cross-shapedsection 36 may be an integral geometric structure machined out of a rodto form a cross-shape integrally connected with an outer hollow cylinder33. This cylinder/cross spring structure may be connected to a motordrive transmission 20 by, e.g., a cable arrangement 37; and may beconnected to other elements at the radially central point of the crosssection by way of, e.g., an end block like that described above. Thecylinder/cross spring structure may be further adapted as shown in FIG.3F. Here, the vertical and horizontal cross sections are machined suchthat there exists no mass at the center crossing point of the sections.Each section 35a-35d thus is integrally connected only to the outercylinder section 33.

In other variations of the spring structure of FIG. 3B, the integralspring may consist of more than two flat sections. For example, three ormore flat sections may be machined along the length of the springstructure, the sections all crossing through the radial midpoint of thespring. The ease of manufacturability and high strength exhibited by thetwo-flat cross spring may, for many applications, be found preferable.

Turning now to force sensing and control schemes provided by theactuation system of the invention, the elastic spring element employedin the actuator system acts as both a force generation mechanism and aforce sensing mechanism. The linearity inherent in the spring enables aforce measurement to be accomplished based on the stretch, or angle oftwist, of the spring. In accordance with the invention, the stretch orangle of twist of the spring is measured directly to determine the forcebeing applied by the spring. This technique requires only one sensor,and therefore requires little calibration, while at the same timeproviding high accuracy through high resolution.

Referring to FIG. 4, in a first direct spring measurement in accordancewith the invention, a potentiometer is employed to produce a resistanceparameter correlated to a torsional spring twist. The potentiometer 50is here connected by way of a potentiometer support 52 to the motorshaft 20. The shaft 54 of the potentiometer is directly connected to theend of the series spring element 16. A 10kΩ Model 140, precisionpotentiometer, available from Spectrol, Inc., is one suitablepotentiometer. In operation, twist of the torsion spring in response toa driving force on motor shaft results in twist of the potentiometershaft and a corresponding development of resistance by thepotentiometer. A measurement of the resistance in, e.g., a resistivebridge circuit, provides an indication of the spring twist andcorresponding spring force.

While this potentiometer sensing scheme is adequate for manyapplications, it has the drawback of requiring precise manual setup andpositioning, and can provide only medium resolution of force readings.In an alternative, preferable sensing scheme, shown in FIGS. 5A and 5B,one or more stain gauges are positioned on the integral cross spring toproduce an indication of the spring force. In this case, the straindeveloped as the spring flats twist is measured by the gauge; the forcemay then in turn be ascertained. The integral cross spring of theinvention is particularly well suited for this type of force measurementbecause the spring flats provide surfaces on which strain gauges may beeasily mounted. For example, as shown in the figures, a strain gauge 60may be positioned directly on one or more flats and on one or both sidesof each flat. This ease of sensor mounting is a unique advantage of thecross spring of the invention.

A full bridge strain gauge circuit is provided by placement of a straingauge on each side of a spring flat, as shown in FIG. 5B. Preferably,the gauges are positioned such that they are aligned with the directionof maximum stress, which is at 45 degrees from the axis of twist fortorsion in the integral cross spring. Strain gauges under the modelnumber CEA-06-062UV-350, available from Micro Measurements, are suitablefor the force sensing scheme of the invention. A strain gaugeconditioner, such as that available from Analog Devices as model 1B31ANmay be employed to measure, amplify, and filter the signal produced bythe gauges. This signal is then differentiated and sampled for use inthe force control scheme of the invention, as explained in detail below.

Although strain gauges are historically known to be difficult to controlin noisy environments such as in the vicinity of motors employingpulse-width-modulation driving, this condition is reduced in theactuator system of the invention because in the integral cross spring ofthe invention, the angle of twist and corresponding spring strain isvery large compared to conventional strain gauge applications. As aresult, the strain gauge signal does not here require a largeamplification factor. In addition, because the integral cross spring isstiff in bending, bending loads on the spring do not have a large impacton the strain readings. In fact, the torsion strains in the spring arefound to be an order of magnitude greater than bending strains in thespring. Finally, while the noise of the system may be increased when thesignal is differentiated by the force control loop, as discussed below,careful EMI shielding of the system adequately reduces the signal noiseto a tolerable level.

The invention is not limited to use of a potentiometer or strain gaugefor sensing force. A conventional hall-effect sensor or other type ofposition transducer that can be mounted directly on the series springelement may be employed as a force transducer. In addition, as will bediscussed in detail below, the elastic actuator design accommodatespositioning of a force transducer in series with the elements of thetransducer at any point along the transducer from the mounting of themotor to the actuator output element. One such transduction scheme isprovided by the sensing arrangement suggested by Levin et al. in U.S.Pat. No. 5,327,790, entitled "Reaction Sensing Torque Actuator," theentirety of which is hereby incorporated by reference. All of the forcetransduction techniques contemplated by the invention provide theability to measure the force generated by an elastic element using onlyone transducer which, as explained, provides many control and precisionadvantages.

Using a strain gauge force sensor, potentiometer force sensor, or othersuitable force sensor for directly sensing the stretch of a linearspring or twist of a torsion spring, the elastic actuator of theinvention provides a control loop for controlling the force generated bythe spring to be applied to a load. Referring to FIG. 6, there is shownthe components of one example control loop 65 in accordance with theinvention. In operation, the actuator spring 16 generates a force by wayof its stretching or twisting action, which is sensed and transduced by,e.g., strain gauges that produce a strain gauge signal 66. This straingauge signal is passed to a sensor board 68, consisting of circuitryprogrammed to amplify, filter, and differentiate the strain gaugesignal. Preferably, the cut off frequency of the strain gauge amplifieris 2 kHz, and the cut off frequency of the strain gauge differentiatoris preferably 100 Hz. These cut off frequencies ensure that there is nosignificant phase roll off over the working frequency of the actuator,which may typically be between, e.g., 0 Hz and 20 Hz.

The conditioned strain gauge signals are then passed from the sensorboard 68 to a motor board 70, which may consist of, e.g., a Motorola6811 micro-controller. This micro-controller is programmed to controlthe motor in response to the spring force for generating a desiredforce. The micro-controller employs, e.g., two analog-to-digitalconverters that are used to sample the conditioned strain gauge signals.The motor board 70 also includes hardware for sensing the encoder signal69 of the motor, and further includes a pulse-width-modulationgeneration circuit and an H-bridge for controlling powering the motor toproduce a desired spring stretch and corresponding spring force.

The motor board 70 is connected by way of, e.g., a differentially-drivencommunication bus 71 to a processor 72, e.g., a Motorola 68332processor. The processor communicates with the motor board for sendingappropriate gain values and set points to the motor board forcontrolling the motor. The Motorola 6811 micro-controller may beprogrammed by, e.g., hand coding in assembly language, which may bedownloaded from a serially-connected computer 74, e.g., a Macintosh PC.The Motorola 68332 processor communicates with the motor board at a rateof up to 400 Hz. The processor may run on, e.g., the programminglanguage L, a subset of Common Lisp, as detailed in "The L Manual," byR.A. Brooks, IS Robotics, 1994. Data from the actuator may be displayedand analyzed in real-time on the computer 74 as the control loopoperates.

Considering now the force control scheme of the invention in moredetail, FIG. 7 illustrates the components of a theoretical control loop80, including a feedback loop 82, a feedforward loop 84, and afeedforward model of the plant, 86 or motor-spring system. Each of theseloops is explained below. FIG. 8 illustrates a force model on which thecontrol loop is based. The motor mass is here given as J_(m), the springstiffness as k_(s), the force on the motor as T_(m), and the outputforce to be applied to a load as T_(l). The movement of the motor shaftand the movement of the load are given as θ_(m) and θ_(l), respectively.The forces balanced between the motor and spring may be expressed as:

    T.sub.m +k.sub.s (θ.sub.l -θ.sub.m)=J.sub.m θ.sub.m 41(2)

and the forces balanced between the load and spring may be expressed as:

    -k.sub.s (θ.sub.l -θ.sub.m)=T.sub.l.           (3)

Taking the Laplace transforms of these expressions provides a directrelationship between the force on the motor and the force on the load,as: ##EQU2## This expression is employed in the force control scheme toindicate what motor force, or torque, is needed to produce a desiredforce, or torque, on the load when the load is moving. The expressionalso defines each of the components of the motor force, which in thecontrol scheme of the invention are in a feedforward section of thecontrol.

If it is assumed that the output of the actuator is clamped, wherebyθ_(l) "=0, then the transfer function between the output torque and themotor torque is given as: ##EQU3## This transfer function between theactual output force, T_(l), and the motor force, T_(m), has no zeros andtwo poles on the imaginary axis, at a frequency ##EQU4## This frequencycorresponds to the natural frequency of the motor mass and serieselastic element.

The transfer function between the output force, T_(l), and the motion ofthe output shaft, θ_(l), as defined in FIG. 8, defines the impedance, Z,of the actuator system, looking from the output of the system. Whilethis transfer function has the same poles as the torque transferfunction in expression (5) above, it also has two zeros at the origin.The impedance function is given as: ##EQU5##

As shown in FIG. 7, the transfer function in expression (5) between theoutput torque and motor torque, together with this expression (6) forthe system impedance define the system model of the plant 86 to becontrolled by the actuator force control scheme.

The feedforward loop is based on a model of how the force on the motormass must vary to produce an output torque on the load when the outputload shaft is moving. This is in fact expressed directly by expression(4) above. The three components on the right side of the expressionindicate the three force control components to be determined; namely,the T_(l) term provides the correct wrap up twisting of the spring,because the force, or torque, to be produced is directly proportional tothe twist angle, the (J_(m) /k_(s))T_(l) " term cancels out the effectof motor mass vibration on the spring, and the J_(m) θ" term moves themotor shaft in correspondence with the load output shaft, therebymaintaining a constant spring twist for a given torque level. Thesecontrol functions are shown in the feedforward block 84 of the controlsystem shown in FIG. 7. Use in the control system of this feedforwardloop, for calculating control, in combination with a feedback loop, tocompensate for errors in the model and for unmodeled disturbances,provides a closed-loop system that provides better control performancethan a control system using a feedback loop alone.

Turning now to the feedback control loop, it is preferable that theactuator control system be stable and passive. This passivity isachieved if the interaction impedance of the system, Z(s), is stable,i.e., has no poles in the right half plane; and if the imaginary part ofZ(jw) is negative for all frequencies. These two requirements result ina system that always absorbs energy from the environment and provides nonet transfer of energy out of the system, and further that the systemimpedance is a stable function of frequency.

Because the actuator force control system is second order, aproportionalderivative, PD, or proportional-integral-derivative, PID,controller is preferred for the feedback loop. While a PD controller maybe stable under certain conditions, the steadystate error of such a loopis high unless the proportional gain component is set quite high.However, the gain cannot be raised without limit due to noise and thesampling rate of the system controller. As a result, for manyapplications a PID controller is preferred. The PID loop provides betterlow-frequency behavior without the need for high gains.

Assuming a PID control of the form K(1+1/(s+τ)T_(i) +sT_(d)), whereT_(i) and T_(d) are the integral and derivative terms, respectively, andτ is a time constant for suppressing the integral action at lowfrequencies, expression (6) above given for system impedance is used toachieve an expression including the PID control as: ##EQU6##

This control law is ensured of meeting the stability criteria givenabove through selection of the values for K and for the constants τ,T_(i), and T_(d). FIG. 7 illustrates the form of the feedback loop 82.

FIG. 9 illustrates a full control system based on the theoreticalcontrol system just described for control of the elastic actuator of theinvention. The system includes five control functions; namely, atransfer function corresponding to the force sensor signal conditioningon the sensor board 68, a PID feedback transfer function 82 to achieve adesired torque, a feedforward transfer function to achieve a desiredtorque, a feedforward function to achieve a desired motor output shaftacceleration 84, and a feed forward model of the motor 85.

This system is like the theoretical control system discussed aboveexcept for elimination of the term that includes the second differentialof the desired force. In operation, it was found that due to difficultyin differentiating very small fixed numbers in software, this term couldnot be adequately implemented. The encoder velocity is here calculatedby differencing successive encoder readings. This value is employedalong with the differentiated strain gauge signal to calculate theacceleration of the output shaft. In the Figure, the parameter "F_(gain)" refers to a gain parameter corresponding to the amount of feedforwardused. In an example implementation of the system, the P_(gain) term wasset at 1908, the I_(gain) term was set at 977, the D_(gain) term was setat 362, and the time constant, τ was set at 11.86 sec. Root locustechniques were used to select these gain values specifically to achievefast performance and reasonable damping while not setting the gains atsuch a high level that system noise could become intolerable.

Considering practical issues relating to the control system, it may bepreferable in some cases to carry out the differentiation of the forcesensor readings, e.g., strain gauge readings, using an analog circuit.For example, in the case of a motor board consisting of a Motorola 6811,the 6811 A/D converter is only 8 bits-wide, and so analogdifferentiation signals of the strain gauge tends to reduce the errorscaused by differentiating small signals in software. The encoder readingon the 6811 is 16 bits-wide, and changes enough during normal operationto accommodate software differentiation. To further accommodate thiscondition, the effective sampling frequency of the encoder may be set ata level of say, e.g., 250 Hz. Note that the 6811 carries out fixed-pointarithmetic, which is why there are several "divide by 256" termsincluded in the control scheme.

In alternative schemes, the entire control system may be provided as ananalog circuit, combination of analog and digital circuitry, orcombination of software and analog or digital circuitry, as will beunderstood by those skilled in the art.

The strain gauge sensor signals were found to preferably be converted toat least a 16 bit-wide signal for the feedback loop calculations, andcorrespondingly, 16 bit-wide, or larger, gain values are preferred. Theoutput from the feedback loop is in the form of an 8 bit-wide valueindicating, e.g., the motor current. Alternatively, the output couldindicate the motor voltage, or other suitable motor control parameter.This value is input to the feedforward motor model, which then producesan 8 bit-wide pulse-width-modulation (PWM) duty cycle command to themotor, along with a 1 bit-wide direction control command applied to themotor.

The motor is driven by an H-bridge, using, e.g., a PWM driver at, e.g.,48 V and 31.25 kHz, or may employ another suitable driver. Thefeedforward model is used to determine the correct voltage to be appliedfor ensuring that the motor current, or voltage, and correspondingtorque, follows that commanded by the control system. Note that thecontrol system in FIG. 9 includes terms for the motor resistance andback emf, but could also preferably include a term for the motorinductance.

The torque control provided by the elastic actuator of the invention inthe example embodiment shown in FIG. 2 is found to be superior toconventional actuator schemes that do not employ a series elasticelement. FIG. 10A illustrates the elastic actuator response to a squarewave in commanded torque when the actuator load element is in contactwith a hard surface, e.g., an aluminum surface. Similarly, FIG. 10Billustrates the elastic actuator response to a square wave in commandedtorque when the actuator load element is in contact with a soft surface,e.g., rubber. Although the response for the soft surface case isslightly less damped than for the hard surface case, neither responseexhibits the instability commonly exhibited by actuators during thistest. FIGS. 10C and 10D illustrate the elastic actuator response to asine wave in commanded torque for a hard surface and soft surface,respectively, and FIG. 10E illustrates the force control performance forfollowing a sine wave command when the output shaft of the actuator,i.e., the load element, is also moving.

Consideration must be given to the impact of the motor movement inresponse to a force control command while the actuator output is moving,as shown in the figure. When the output of the actuator is moving, themotor must not only move to achieve a desired spring compression ortwist, but also move along together with the output such that a constantforce is maintained at the output. The actual motor motion is thus inthis case the sum of that required to generate the desired force andthat required to follow the actuator output path. As the desired torquewaveform command and the actuator output motion change in size and phaseduring normal operation, the extra motor control required to accommodatethis motion may add either constructively or destructively to the actualmotor motion, either increasing or decreasing the bandwidth of the forcecontrol.

In contrast, in the case of a conventional, stiff actuator, the onlymotion required of the motor shaft is that of the actuator output, e.g.,that of an actuator output shaft. Based on the expressions for systemimpedance, Z, discussed above, it is found that for low frequencies ofactuator output motion, the elastic actuator of the invention provides amuch wider dynamic range, i.e., range between minimum force and maximumforce, than that provided by a stiff, conventional actuator. As thefrequency of output motion increases toward the characteristic naturalfrequency of the elastic actuator, there then exists a wide range ofimpedances for which the elastic actuator performs better than acorresponding stiff actuator. At relatively high frequencies, theelastic actuator behaves like a spring, and so is substantial better atgenerating the necessary impedances than a corresponding stiff actuator.

The bandwidth over which the elastic actuator out-performs acorresponding conventional, stiff actuator may be made more broad usingan adaptation of the elastic actuator design as shown in FIG. 11. Herethe elastic actuator 10 consists of, e.g., two spring elements 16a, 16b,connected in parallel between corresponding motors 12a, 12b and a loadelement 18, or may include more than two elastic elements. Each springelement preferably is characterized by a different spring stiffness. Oneof the motor-spring combinations may be specified with, e.g., a lowstiffness spring, to provide superior low-frequency behavior, while theother spring may, e.g., be stiffer, for providing superior highfrequency behavior. Such a multi-spring/motor actuator scheme is able toprovide a wide-bandwidth system response because the springs togetherprovide a non-stiff coupling between the motors and the load, therebyeffectively isolating each motor from the load.

Clearly the superior force control, compliance, stability, and shockprotection provided by the elastic actuator of the invention lends theactuator to a wide range of applications. For example, the elasticactuator is well-suited for use as a robot arm, hand, or leg, along withmany other actuation applications in which unstructured environments areto be interfaced. While the discussion above primarily focused on arotary actuator design employing a torsional spring, many other elasticactuator designs are contemplated by the invention. For example, asshown in FIG. 12A, a linear motor 100 and linear spring 102 combinationmay be employed with a load end element 18 in an elastic actuator inaccordance with the invention. Here, a lead screw (not shown) or othermechanism may be employed to couple the motor with the spring element.

In an alternative embodiment, applicable to both linear and rotary driveactuators, the motor mechanism be itself be supported as an end elementby the actuator spring. This scheme is illustrated in FIG. 12B. Here,one end of the spring is attached to ground by way of, e.g., a groundingblock or plate 104. The other end of the spring is linked to a motor 12,perhaps through a transmission. The motor 12 is in turn connected to theactuator load element 18. In this case then, the spring element supportsthe weight of both the actuator load and the actuator motor. Thisarrangement may be employed for either rotary or linear motor-basedelastic actuators.

Turning to FIG. 13, there is shown an alternative elastic actuator inaccordance with the invention. Here a pulley-based elastic actuator 110is formed of a motor 112, such as a rotary motor, connected by way of,e.g. a shaft 114, to a pulley system. The pulley system provides a drivepulley 116 connected by way of one or more elastic spring elements 118a,118b, to a load pulley 120. Rotation of the motor shaft 114 acts to turnthe drive pulley 116 and exert a force to the load pulley by way of thesprings 118. The springs may be made up of, e.g., standard linear springmaterial; and if desired for particular applications, only one springneed be positioned along the pulley line between the drive and loadpulleys, on either of the sides of the pulley line.

This elastic pulley actuator scheme may be adapted like those justdiscussed by way of attaching a load pulley, rather than the drivepulley, at the motor end of the actuator system and supporting both theload pulley and the motor by the spring element or elements.

In general, there are many other alternative embodiments of an elasticpulley actuator like that discussed above, where a cable, or tendon, maybe employed, as in the pulley system, to transmit torque between theoutput of a motor transmission and a joint some distance away from themotor. This scheme has the advantage of keeping the mass, andcorresponding inertia, of the motor and its attending gearbox away fromthe joint. By locating the motor remotely the robot structure has lessinertia and is lighter, and accordingly, has less inertia to support andcan accelerate more quickly. In such an elastic tendon system, a seriesspring element may be provided by the elasticity of the tendon cableitself, or, if this elasticity is insufficient for a given application,may be achieved by inserting elastic elements, e.g., extension springs,in series with the cable, as shown in the figure. Because tendons can ingeneral not provide compressive force, it is necessary to employ anelastic element in series with each of two cables if achievement ofbi-directional torque is desired. In this case, in general, it ispreferable that the cable loop be tensioned to slightly more thanone-half of the expected applied force, so that under maximum torque ineither direction, neither cable will go slack.

An ancillary advantage provided by series elasticity in a tendon systemis that the elastic element tends to lower the overall sensitivity ofthe system to tendon stretching. Typically, tendons stretch as they age.With an added spring element, any elasticity in the tendon is dominatedby that of spring element, whereby small changes in tendon length do notsignificantly alter the tendon tension.

The torque generated by a series spring element in a tendon system maybe sensed by transducing tension of a tendon. This may be accomplisheddirectly by a series element, or may be accomplished indirectly by,e.g., an idler wheel that deflects the tendon and measures theperpendicular force applied. Note that although two tendons and twoelastic elements may be employed for a given application, the forcecontrol scheme of the invention requires only that the tension on atleast one tendon side be measured. If a series force transducer isemployed in a tendon system, it is preferable to place the forcetransducer close to the final attachment point of the tendon, wherebythe motion of the transducer relative to the final supporting link issmall, and accordingly, wires with a small amount of play may beattached.

The force transducer for a tendon system may be embodied as any of theforce transducers described previously, e.g., as a strain gauge, oralternatively, may employ a stretch transducer. Such a stretchtransducer is provided by, e.g., a potentiometer, a strain gauge, aconventional hall effect sensor, or any other type of positiontransducer that may be mounted directly across the spring element.Alternatively, an idler wheel exhibiting frictional contact with atendon may be positioned along a tendon between the motor and the springelement for sensing motion relative to the final attachment point. Suchan idler wheel may be connected with only one side of the tendon or withboth tendons. Several examples of such schemes using an idler wheel willbe illustrated in turn below.

In all such actuator systems employing an idler pulley configuration inaccordance with the invention, an actuator output link is supported by,e.g., a revolute bearing connecting the output link to the idler pulleyby way of its shaft. Tendons are connected between a capstan positionedat the output of a motor gear train and the idler pulley, around whichthey are wrapped. One or more series spring elements are positionedbetween the idler pulley and the attachment point of the cable on theoutput link. Alternatively, the spring element may be placed between theidler pulley and the capstan, in which case, the idler pulley ispreferably rigidly attached to the output link. In this configuration, aforce transducer must be positioned to move with the tendon, however,while in the first case given, a force sensor may be positioned fixedlywith respect to the output link.

Turning now to FIG. 14A, in a first pulley-tendon elastic actuator 120,a capstan 122 supports a tendon 124 wrapped around an idler pulley 126and then connected to an actuator output link member 128. Series springelements 16a, 16b are positioned along the tendon and connected to thelink member. In a first force transduction technique, the stretch ofspring elasticity is directly measured by way of a linear transducer 130connected across the elasticity. Such a transducer may embody, e.g., apotentiometer, digital encoder, hall effect proximity sensor, or otherposition transducer. Note that the sensor measures only spring motion,not overall motion of the entire actuator system. If insensitivity tochanges in overall tendon length is desired, as might be produced by,e.g., machining tolerances, two transducers may be used on both springmembers, and the outputs subtracted by a standard differential amplifierprovided by a section of the force control loop.

In a second tendon-idler pulley elastic actuator, shown in FIG. 14B, therevolute motion of the idler pulley is measured with respect to theactuator output link position to determine the actuator spring stretchand corresponding force. In this case, when the series spring membersstretch differentially, the idler pulley experiences motion relative tothe output link. This relative motion may be detected by a revolutetransducer 132, embodying, e.g., a potentiometer, digital shaft encoder,or other suitable rotary transducer. Alternatively, an additional idlerpulley (not shown) may be mounted, by way of a bearing, to the outputlink in frictional contact with one or both of the tendon sides betweenthe idler pulley and the spring members; a shaft encoder or other rotarysensor is then employed to sense relative motion of this second pulley.

Turning now to FIG. 14C, there is shown an elastic tendon actuator inwhich torque is measured by measuring the reaction torque of the motor12 and gear train 14. This is accomplished using strain gauges 134a,134b positioned at the motor housing 12. This configuration provides anadvantage in that the sensors never move, but has the disadvantage thattorque components due to the inertia of the motor are included in themeasurement. Such torque components can be removed from the forcemeasurement by conventional compensation techniques in the feed forwardloop of the control system. An additional advantage provided by thisconfiguration is the flexibility to position a series spring member 16a,16b, either before or after the idler pulley 126.

Alternatively, as shown in FIG. 14D, a torsion spring 136 and associatedstrain gauges 138a, 138b may be positioned with respect to the linkagebetween the gear train 14 and capstan 122 to sense force in the actuatorsystem. Such a torsion spring 135 may take a form like that of thetorsion springs previously discussed, or any suitable form. Like thedesign of FIG. 14C, this design provides flexibility in positioning theseries springs either before or after the idler wheel. The combinationtorsion spring and the series elastic tension springs together providethe ability to tailor the overall actuator compliance provided by eachof the springs. For example, in one limit, all of the system compliancemay be provided by the torsion spring, in which case the tension springsare not needed. At the other extreme, the torsion spring may be verystiff and the tension springs may provide substantial compliance. Anybalance between these extremes may be selected to achieve a desiredcompliance balance for any given application.

A direct tendon tension measurement may alternatively be employed asshown in FIG. 14E. Here one or two load cell strain gauges 140 areconnected between the end of the tendon and the output link member 128.If insensitivity to common-mode changes in overall cable tension isdesired, the output of two such strain gauges may be subtracted by adifferential amplifier, as discussed above. Alternatively, the straingauges, which are usually configured as a bridge, may be distributed onboth sides of the output link 128 such that differential subtractionoccurs in the bridge itself.

In a final example, shown in FIG. 14F, the system force is determined bythe force required to deflect the tendon. Such a perpendicular force isdirectly related to the tension in the tendon. The measurement may beaccomplished by, e.g., strain gauges 142 positioned along the tendon ata point where a perpendicular force is introduced by way of, e.g.,pulleys 144, 146, and 148. The pulley arrangement may be located at anypoint along the tendon. Use of two strain gauges may be employed toachieve insensitivity to common mode tension changes in the two tendonsides.

Other elastic tendon configurations are within the scope of theinvention. The invention is not limited to specific tendonconfigurations or types of configurations; but rather, is characterizedby configurations that provide series elasticity, the ability to measuretension in the tendon system, and the ability to produce force by way ofthe series elasticity.

From the foregoing, it is apparent that the elastic actuator designs,force control schemes, and spring configurations described above notonly achieve improved actuator force control, among other advantages,but do so in a particularly effective and efficient manner. It isrecognized, of course, that those skilled in the art may make variousmodifications and additions to the preferred embodiments described abovewithout departing from the spirit and scope of the present contributionto the art. Accordingly, it is to be understood that the protectionsought to be afforded hereby should be deemed to extend to the subjectmatter of the claims and all equivalents thereof fairly within the scopeof the invention.

We claim:
 1. An elastic actuator having gone control, the actuatorcomprising:a motor; a motor drive transmission connected at an output ofthe motor; at least one elastic element connected in series with themotor drive transmission, the at least one elastic element positioned tofully support along either direction of an actuation axis, a loadconnected at at least one output of the actuator, as the load isactuated along either direction of the actuation axis, a single forcetransducer positioned at a point between a mount for the motor and atleast one output of the actuator, the force transducer generating aforce signal indicating force applied by the elastic element to at leastone output of the actuator; and an active feedback force controllerconnected between the force transducer and the motor for controlling themotor, based on the force signal, to deflect the elastic element anamount that produces a desired actuator output force, the output forcebeing substantially independent of load motion.
 2. The elastic actuatorof claim 1 wherein the force transducer comprises a strain gauge.
 3. Theelastic actuator of claim 1 wherein the force transducer comprises astrain gauge positioned on the elastic element.
 4. The elastic actuatorof claim 1 wherein the force transducer comprises a potentiometer. 5.The elastic actuator of claim 1 wherein the elastic element comprises alinear spring.
 6. The elastic actuator of claim 1 wherein elasticelement comprises a torsional spring.
 7. The elastic actuator of claim 1wherein the force signal generated by the force transducer is based ondeflection of the elastic element.
 8. The elastic actuator of claim 1wherein the force transducer comprises a magnetic position transducer.9. The elastic actuator of claim 1 wherein the force transducercomprises an optical position sensor.